(eng): In a recent paper we have extended the concept of piecewise linear histogram (PLH) introduced by Beirlant, Berlinet and Gyorfi. The disadvantage of the PLH is that, in many models with probability closed to 1, it takes on negative values with probability close to one. We have shown that for all models satisfying mild assumptions, the class of our generalized piecewise linear histograms (GPLH's) contains a bona fide density with probability tending to 1 as the sample size n increases to infinity.